Refracting Telescopes Astrophysics Lesson 2

Homework No homework except to revise for the mock exam on Friday!

Astronomy Picture of the Day

Today’s Objectives Draw ray diagram to show the image formation in normal adjustment Calculate angular magnification in normal adjustment also using focal lengths of the lenses.

Clarification A real image is formed when light rays from an object are made to pass through another point in space. A virtual image is formed when light rays from an object appear to have come from another point in space.

The Refracting Telescope The refracting telescope works by bending light with lenses. The objective lens makes a small real image of the object while the eyepiece lens acts as a magnifying glass.

The Refracting Telescope The following factors are important in making a good quality instrument: Lens quality: bad lenses, bad image Lens diameter: brightness and detail observed depend on the area. A 12 cm lens can resolve detail nine times better than a 4 cm lens. Angular magnification. The diagram shows the telescope when it is set up normally (normal adjustment).

Refracting Telescope

Light from object A (blue lines) meets at the principal focus of the objective lens. It then spreads out until it meets the eyepiece. The eyepiece is set at the focal length away from its principal focus. Parallel rays emerge from the eyepiece. At the same time parallel rays from object B arrives at the objective at a small angle α to the axis. The light is focused onto the focal plane. It then passes through the eyepiece to emerge as parallel rays. The angle of these parallel rays is β to the parallel rays from A.

Angular Magnification The angular magnification can be worked out by the simple formula: where α and β are small angles in radians. The angle α is the angle subtended by the object to the unaided eye. The angle β is the angle subtended by the image to the eye.

Magnification The magnification can also be shown to be related to the focal lengths of the lenses by: Where f 0 is the focal length of the objective lens And f e is the focal length of the eyepiece lens.

Question In a telescope the eyepiece has a focal length of 2 cm and the objective has a focal length of 220 cm. What is the magnification? If the moon subtends an angle of 8.8 × rad to the naked eye, what would the angle be for the image of the moon observed through the telescope?

Answer Magnification = f o /f e = 220/2 = 110 Angle subtended by the Moon = 8.8 x rad x 110 = 0.97 rad

Note The telescope shown above makes an inverted image. To make the image the right way up we need to put in a third lens at the principal focus of the objective lens, but we won't go into that at this point. Often doesn’t matter for astronomical purposes.

Summary Refracting telescopes use converging lenses Lenses make images of objects that can be worked out using Ray diagrams Or the lens formula (1/f = 1/u + 1/v) The telescope consists of two lenses set at a distance = f o + f e Magnification = β/α = f o /f e